Multiple frequency atomic force microscopy

ABSTRACT

An apparatus and technique for extracting information carried in higher eigenmodes or harmonics of an oscillating cantilever or other oscillating sensors in atomic force microscopy and related MEMs work is described.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of U.S. Ser. No.11/544,130 filed Oct. 5, 2006, now U.S. Pat. No. 7,603,891 issued Oct.20, 2009, which claims priority of U.S. Provisional Application No.60/795,151, filed on Apr. 25, 2006, U.S. Provisional Application No.60/811,264, filed on Jun. 5, 2006, and U.S. Provisional Application No.60/839,749, filed on Aug. 24, 2006, the disclosures of which areincorporated fully herein by reference.

BACKGROUND OF THE INVENTION

For the sake of convenience, the current description focuses systems andtechniques that may be realized in a particular embodiment ofcantilever-based instruments, the atomic force microscope (AFM).Cantilever-based instruments include such instruments as AFMs, 3Dmolecular force probe instruments, high-resolution profilometers(including mechanical stylus profilometers), surface modificationinstruments, chemical or biological sensing probes, and micro-actuateddevices. The systems and techniques described herein may be realized insuch other cantilever-based instruments.

An AFM is a device used to produce images of surface topography (and/orother sample characteristics) based on information obtained fromscanning (e.g., rastering) a sharp probe on the end of a cantileverrelative to the surface of the sample. Topographical and/or otherfeatures of the surface are detected by detecting changes in deflectionand/or oscillation characteristics of the cantilever (e.g., by detectingsmall changes in deflection, phase, frequency, etc., and using feedbackto return the system to a reference state). By scanning the proberelative to the sample, a “map” of the sample topography or other samplecharacteristics may be obtained.

Changes in deflection or in oscillation of the cantilever are typicallydetected by an optical lever arrangement whereby a light beam isdirected onto the cantilever in the same reference frame as the opticallever. The beam reflected from the cantilever illuminates a positionsensitive detector (PSD). As the deflection or oscillation of thecantilever changes, the position of the reflected spot on the PSDchanges, causing a change in the output from the PSD. Changes in thedeflection or oscillation of the cantilever are typically made totrigger a change in the vertical position of the cantilever baserelative to the sample (referred to herein as a change in the Zposition, where Z is generally orthogonal to the XY plane defined by thesample), in order to maintain the deflection or oscillation at aconstant pre-set value. It is this feedback that is typically used togenerate an AFM image.

AFMs can be operated in a number of different sample characterizationmodes, including contact mode where the tip of the cantilever is inconstant contact with the sample surface, and AC modes where the tipmakes no contact or only intermittent contact with the surface.

Actuators are commonly used in AFMs, for example to raster the probe orto change the position of the cantilever base relative to the samplesurface. The purpose of actuators is to provide relative movementbetween different parts of the AFM; for example, between the probe andthe sample. For different purposes and different results, it may beuseful to actuate the sample, the cantilever or the tip or somecombination of both. Sensors are also commonly used in AFMs. They areused to detect movement, position, or other attributes of variouscomponents of the AFM, including movement created by actuators. For thepurposes of the specification, unless otherwise specified, the term“actuator” refers to a broad array of devices that convert input signalsinto physical motion, including piezo activated flexures, piezo tubes,piezo stacks, blocks, bimorphs, unimorphs, linear motors,electrostrictive actuators, electrostatic motors, capacitive motors,voice coil actuators and magnetostrictive actuators, and the term“position sensor” or “sensor” refers to a device that converts aphysical parameter such as displacement, velocity or acceleration intoone or more signals such as an electrical signal, including capacitivesensors, inductive sensors (including eddy current sensors),differential transformers (such as described in co-pending applicationsUS20020175677A1 and US20040075428A1, Linear Variable DifferentialTransformers for High Precision Position Measurements, andUS20040056653A1, Linear Variable Differential Transformer with DigitalElectronics, which are hereby incorporated by reference in theirentirety), variable reluctance, optical interferometry, opticaldeflection detectors (including those referred to above as a PSD andthose described in co-pending applications US20030209060A1 andUS20040079142A1, Apparatus and Method for Isolating and MeasuringMovement in Metrology Apparatus, which are hereby incorporated byreference in their entirety), strain gages, piezo sensors,magnetostrictive and electrostrictive sensors.

In both the contact and AC sample-characterization modes, theinteraction between the stylus and the sample surface induces adiscernable effect on a probe-based operational parameter, such as thecantilever deflection, the cantilever oscillation amplitude, the phaseof the cantilever oscillation relative to the drive signal driving theoscillation or the frequency of the cantilever oscillation, all of whichare detectable by a sensor. In this regard, the resultantsensor-generated signal is used as a feedback control signal for the Zactuator to maintain a designated probe-based operational parameterconstant.

In contact mode, the designated parameter may be cantilever deflection.In AC modes, the designated parameter may be oscillation amplitude,phase or frequency. The feedback signal also provides a measurement ofthe sample characteristic of interest. For example, when the designatedparameter in an AC mode is oscillation amplitude, the feedback signalmay be used to maintain the amplitude of cantilever oscillation constantto measure changes in the height of the sample surface or other samplecharacteristics.

The periodic interactions between the tip and sample in AC modes inducescantilever flexural motion at higher frequencies. The results of theseinteractions probe a variety of tip and sample mechanical propertiesincluding conservative and dissipative interactions. The prior art hasdiscussed the flexural response of a cantilever at higher frequencies asnonlinear interactions between the tip and the sample. Prior art hasexplored the amplitude and phase at numerous higher oscillationfrequencies and related these signals to the mechanical properties ofthe sample.

Unlike the plucked guitar strings of elementary physics classes,cantilevers normally do not have higher oscillation frequencies thatfall on harmonics of the fundamental frequency. The first three modes ofa simple diving board cantilever, for example, are at the fundamentalresonant frequency (f₀), 6.19 f₀ and 17.5 f₀. An introductory text incantilever mechanics has many more details. Through careful engineeringof cantilever mass distributions, a class of cantilevers has beendesigned hose higher modes do fall on higher harmonics of thefundamental resonant frequency. Cantilevers driven at the fundamentalexhibit enhanced contrast, based on their simulations on mechanicalproperties of the sample surface. This approach is has the disadvantageof requiring costly and difficult to manufacture special cantilevers.

In some very early work, cantilever was at two frequencies. Thecantilever response at the lower, non-resonant frequency was used as afeedback signal to control the surface tracking and produced atopographic image of the surface. The response at the higher frequencywas used to characterize differences in the non-contact forces above theSi and photo-resist on a patterned sample.

Recently, Rodriguez and Garcia published a theoretical simulation of anon-contact, attractive mode technique where the cantilever was drivenat its two lowest eigenfrequencies. In their simulations, they observedthat the phase of the second mode had a strong dependence on the Hamakerconstant of the material being imaged, implying that this techniquecould be used to extract chemical information about the surfaces beingimaged. Crittenden et al. have explored using higher harmonics forsimilar purposes.

SUMMARY OF THE INVENTION

Cantilevers are continuous flexural members with a continuum ofvibrational modes. The present invention, Multiple Frequency AtomicForce Microscopy, describes different apparatus and methods for drivingthe cantilever simultaneously at or near two or more of the cantilevervibrational eigenmodes and the useful information revealed in theresulting images and measurements.

Past work with AC mode AFMs has been concerned with higher vibrationalmodes in the cantilever, with linear interactions between the tip andthe sample. The present invention, however, is centered aroundnon-linear interactions between the tip and sample that couple energybetween two or more different cantilever vibrational modes, usually keptseparate in the case of linear interactions. Observing the response ofthe cantilever at two or more different vibrational modes has someadvantages in the case of even purely linear interactions however. Forexample, if the cantilever is interacting with a sample that has somefrequency dependent property, this may show itself as a difference inthe mechanical response of the cantilever at the different vibrationalmodes.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 Preferred embodiment for probing multiple eigenmodes of acantilever.

FIG. 2 Apparatus used for exciting voltage dependent motion in thecantilever probe.

FIG. 3 Arrangement used for probing an active device.

FIG. 4 Phase and amplitude shifts of the fundamental eigenmode with andwithout the second eigenmode being driven.

FIG. 5 Images of collagen fibers taken with the preferred embodiment.

FIGS. 6 and 7 show Two dimensional histogram plots of the amplitude andphase for the first and second eigenmodes.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 is a block diagram of a preferred embodiment of an apparatus forprobing multiple eigenmodes of a cantilever in accordance with thepresent invention. The sample 1010 is positioned below the cantileverprobe 1020. The chip of the cantilever probe 1030 is driven by amechanical actuator 1040, preferrably a piezoelectric actuator, butother methods to induce cantilever motion known to those versed in theart could also be used. The motion of the cantilever probe 1030 relativeto the frame of the microscope 1050 is measured with a detector 1060,which could be an optical lever or another method known to those versedin the art. The cantilever probe 1030 is moved relative to the sample1010 by a scanning apparatus 1070, preferably a piezo/flexurecombination, but other methods known to those versed in the art couldalso be used.

The motion imparted to the cantilever chip 1030 by actuator 1040 iscontrolled by excitation electronics that include at least two frequencysynthesizers 1080 and 1090. There could be additional synthesizers ifmore than two cantilever eigenmodes are to be employed. The signals fromthese frequency synthesizers could be summed together by an analogcircuit element 1100 or, preferably, a digital circuit element thatperforms the same function. The two frequency synthesizers 1080 and 1090provide reference signals to lockin amplifiers 1110 and 1120,respectively. In the case where more than two eigenmodes are to beemployed, the number of lockin amplifiers will also be increased. Aswith other electronic components in this apparatus, the lockinamplifiers 1110 and 1120 can be made with analog circuitry or withdigital circuitry or a hybrid of both. For a digital lockin amplifier,one interesting and attractive feature is that the lockin analysis canbe performed on the same data stream for both eigenmodes. This impliesthat the same position sensitive detector and analog to digitalconverter can be used to extract information at the two distincteigenmodes.

The lockin amplifiers could also be replaced with rms measurementcircuitry where the rms amplitude of the cantilever oscillation is usedas a feedback signal There are a number of variations in the FIG. 1apparatus that a person skilled in the art could use to extractinformation relative to the different eigenmodes employed in the presentinvention. Preferably, a direct digital synthesizer (DDS) could be usedto create sine and cosine quadrature pairs of oscillating voltages, eachat a frequency matched to the eigenmodes of the cantilever probe 1030that are of interest. Then the amplitude and phase of each eigenmode canbe measured and used in a feedback loop calculated by the controller1130 or simply reported to the user interface 1140 where it isdisplayed, stored and/or processed further in an off-line manner.Instead of, or in addition to, the amplitude and phase of the cantilevermotion, the quadrature pairs, usually designated x and y, can becalculated and used in a manner similar to the amplitude and phase.

In one method of using the FIG. 1 apparatus, the cantilever is driven ator near two or more resonances by the single “shake” piezo. Operating ina manner similar to AC mode where the cantilever amplitude is maintainedconstant and used as a feedback signal, but employing the teachings ofthe present invention, there are now a number of choices for thefeedback loop. Although the work here will focus on using the amplitudeof the fundamental (A₀), we were able to successfully image using one ofthe higher mode amplitudes (A_(i)) as a feedback signal as well as a sumof all the amplitudes A₀+A₁+ . . . . One can also choose to exclude oneor more modes from such a sum. So for example, where three modes areemployed, the sum of the first and second could be used to operate thefeedback loop and the third could be used as a carry along signal.

Because higher eigenmodes have a significantly higher dynamic stiffness,the energy of these modes can be much larger that that of lowereigenmodes.

The method may be used to operate the apparatus with one flexural modeexperiencing a net attractive force and the other a net repulsive force,as well as operating with each mode experiencing the same net sign offorce, attractive or repulsive. In this manner, it is possible toseparate short and long range forces, providing additional informationabout sample properties and allowing, for example, the simultaneous andseparated measurement of topography and magnetic or electric fields.

One preferred technique for using the aforesaid method is as follows.First, excite the probe tip at or near a resonant frequency of thecantilever with a free amplitude A₁₀ small enough so that the cantileverwill interact with the surface in a non-contact mode; that is the phasep₁ will be greater than p₁₀. In this mode, the cantilever is nottouching the surface; it turns around before it interacts withsignificant repulsive forces.

Second, reduce the relative distance in the Z direction between the baseof the cantilever and the sample surface so that the amplitude of theprobe tip A₁ is affected by the proximity of the sample surface andsetup a feedback loop that controls the distance between the base of thecantilever and the sample surface so that the amplitude maintained at anessentially constant value during scanning.

Third, keeping the first eigenmode drive and surface controllingfeedback loop with the same values, excite a second eigenmode of thecantilever at an amplitude A₂. Increase A₂ until the second eigenmodephase p₂ shows that the cantilever eigenmode is interacting withpredominantly repulsive forces; that is, that p₂ is less than p₂₀, thefree second eigenmode phase. This second amplitude A₂ is not included inthe feedback loop and should be allowed to freely roam over a largerange of values. In fact, it is typically better if variations in A₂ canbe as large as possible, ranging from 0 to A₂₀, the free secondeigenmode amplitude.

Fourth, the feedback amplitude and phase A₁ and p₁ as well as the carryalong second eigenmode amplitude and phase should be measured anddisplayed.

Alternatively, the drive amplitude and/or phase of the second frequencycan be continually adjusted to maintain the second amplitude and/orphase at an essentially constant value. In this case, it is useful todisplay and record the drive amplitude and/or frequency required tomaintain the second amplitude and/or phase at an essentially constantvalue.

A second preferred technique for using the aforesaid method follows thefirst two steps of first preferred technique just described and thencontinues with the following two steps:

Third, keeping the first eigenmode drive and surface controllingfeedback loop with the same values, excite a second eigenmode (orharmonic) of the cantilever at an amplitude A₂. Increase A₂ until thesecond eigenmode phase p₂ shows that the cantilever eigenmode isinteracting with predominantly repulsive forces; that is, that p₂ isless than p₂₀, the free second eigenmode phase. At this point, thesecond eigenmode amplitude A₂ should be adjusted so that the firsteigenmode phase p₁ becomes predominantly less than the free phase p₁₀.In this case, the adjustment of the second eigenmode amplitude A₂ hasinduced the first eigenmode of the cantilever to interact with thesurface in a repulsive manner. As with the first preferred technique,the second amplitude A₂ in not used in the tip-surface distance feedbackloop and should be allowed range widely over many values.

Fourth, the feedback amplitude and phase A₁ and p₁ as well as the carryalong second eigenmode amplitude and phase should be measured anddisplayed.

Either of the preferred techniques just described could be performed ina second method of using the FIG. 1 apparatus where the phase of theoscillating cantilever is used in a feedback loop where the oscillationfrequency is varied to maintain phase essentially constant. In thiscase, it is preferable to use the oscillation frequency as an input intoa Z-feedback loop that controls the cantilever-sample separation.

Relative changes in various parameters such as the amplitude and phaseor in-phase and quadrature components of the cantilever at thesedifferent frequencies could also be used to extract information aboutthe sample properties.

A third preferred technique for using the aforesaid method provides analternative for conventional operation in a repulsive mode, that iswhere the tip is experiencing a net repulsive force. The conventionalapproach for so operating would be to use a large amplitude incombination with a lower setpoint, and a cantilever with a very sharptip. Using the third preferred technique, however, the operator begins,just as with the first two techniques, by choosing an amplitude andsetpoint for the fundamental eigenmode that is small enough to guaranteethat the cantilever is experiencing attractive forces, that is, that thecantilever is in non-contact mode. As noted before, this operationalmode can be identified by observing the phase of the cantileveroscillation. In the non-contact case, the phase shift is positive,implying that the resonant frequency has been lowered. With theseconditions on the first eigenmode, the second eigenmode excitation canbe introduced and the amplitude, drive frequency and, if applicable,setpoint, chosen with the following considerations in mind:

1. Both eigenmodes are in the attractive mode, that is to say that thephase shift of both modes is positive, implying both eigenmodefrequencies have been shifted negatively by the tip-sample interactions.Generally, this requires a small amplitude for the second eigenmode.

2. The fundamental eigenmode remains attractive while the secondeigenmode is in a state where the tip-sample interactions cause it to bein both attractive and repulsive mode as it is positioned relative tothe surface.

3. The fundamental eigenmode is in an attractive mode and the secondeiegenmode is in a repulsive mode.

4. In the absence of any second mode excitation, the first eigenmode isinteracting with the surface in the attractive mode. After the secondeigenmode is excited, the first eigenmode is in a repulsive mode. Thischange is induced by the addition of the second eigenmode energy. Thesecond eigenmode is in a state where the tip-sample interactions causeit to be attractive and/or repulsive.

5. The first eigenmode is in a repulsive mode and the second mode is ina repulsive mode.

The transition in the first mode response from attractive to repulsivemode which is induced by the second mode excitation is illustrated inFIG. 4, where the amplitude and phase of the first and second modes areplotted as a function of the distance between the base of the cantileverand the sample surface. The point where the cantilever tip begins tointeract significantly with the surface is indicated with a solid line4000. The two curves in the lower half of FIG. 4 show that the amplitude4010 of the fundamental of a cantilever decreases as the cantileverstarts to interact with the surface and the associated phase 4020 showsa positive shift, consistent with overall attractive interactions. Forthese curves, the second mode is not excited and therefore the secondmode amplitude is zero and the amplitude and phase are not shown. Thesecond mode amplitude 4030 and phase 4040 when this mode is excited areplotted in the upper half of FIG. 4. Excitation of the second modeinduces a notable change in the fundamental mode amplitude 4050 and,more strikingly, the fundamental mode phase 4060. The fundamental modephase 4060 in fact shows a brief positive excursion, but thentransitions to a negative phase shift, indicating an overall repulsiveinteraction between the tip and sample. The free amplitude 4050 of thefirst mode is virtually identical in both cases, the only difference inthe measurement is the addition of energy exciting the higheroscillatory mode. This excitation is sufficient to drive the fundamentalmode into overall repulsive interaction with the sample surface. Thephase curve of the second mode indicates that it is also interactingoverall repulsively with the sample surface.

More complicated feedback schemes can also be envisioned. For example,one of the eigenmode signals can be used for topographical feedbackwhile the other signals could be used in other feedback loops. Anexample would be that A₁ is used to control the tip-sample separationwhile a separate feedback loop is used to keep A₂ at an essentiallyconstant value rather than allowing it to range freely over many values.A similar feedback loop could be used to keep the phase of the secondfrequency drive p₂ at a predetermined value with or without the feedbackloop on A₂ being implemented.

As another example of yet another type of feedback that could be used,Q-control can also be used in connection with any of the techniques forusing the aforesaid method. Using Q-control on any or all of the modesemployed can enhance their sensitivity to the tip-sample forces andtherefore mechanical or other properties of the sample. It can also beused to change the response time of the modes employed which may beadvantageous for more rapidly imaging a sample. For example, the valueof Q for one mode could be increased and the value for anotherdecreased. This may enhance the result of mixed attractive/repulsivemode imaging because it is generally easier to keep one eigenmodeinteracting with the sample in repulsive mode with a reduced Q-value or,conversely, in attractive mode with an enhanced Q-value. By reducing theQ-value of the lowest mode and enhancing the Q-value of the next mode,it is possible to encourage the mixed mode operation of the cantilever;the zeroth mode will be in repulsive mode while the first mode will morelikely remain in attractive mode. Q-control can be implemented usinganalog, digital or hybrid analog-digital electronics. It can beaccomplished using an integrated control system such as that in theAsylum Research Corporation MFP-3D Controller or by after-market modulessuch as the nanoAnalytics Q-box.

In addition to driving the cantilever at or near more than oneeigenmode, it is possible to also excite the cantilever at or near oneor more harmonics and/or one or more eigenmodes. It has been known forsome time that nonlinear interactions between the tip and the sample cantransfer energy into cantilever harmonics. In some cases this energytransfer can be large but it is usually quite small, on the order of apercent of less of the energy in the eigenmode. Because of this, theamplitude of motion at a harmonic, even in the presence of significantnonlinear coupling is usually quite small. Using the methods describedhere, it is possible to enhance the contrast of these harmonics bydirectly driving the cantilever at the frequency of the harmonic. Tofurther enhance the contrast of this imaging technique it is useful toadjust the phase of the higher frequency drive relative to that of thelower. This method improves the contrast of both conventionalcantilevers and the specially engineered “harmonic” cantilevers.

On many samples, the results of imaging with the present invention aresimilar to, and in some cases superior to, the results of conventionalphase imaging. However, while phase imaging often requires a judiciouschoice of setpoint and drive amplitude to maximize the phase contrast,the method of the present invention exhibits high contrast over a muchwider range of imaging parameters. Moreover, the method also works influid and vacuum, as well as air and the higher flexural modes showunexpected and intriguing contrast in those environments, even onsamples such as DNA and cells that have been imaged numerous timesbefore using more conventional techniques.

The superior results of imaging with the present invention may be seenfrom an inspection of the images. An example of is shown in FIG. 5. Forthis example, the FIG. 1 apparatus was operated using the fundamentaleigenmode amplitude as the error signal and the second eigenmode as acarry-along signal. The topography image 5010 in FIG. 5 shows collagenfibers on a glass surface, an image typical of results with conventionalAC mode from similar samples. The fundamental eigenmode amplitude image5020 is relatively similar, consistent with the fundamental eigenmodeamplitude being used in the feedback loop. The fundamental eigenmodephase channel image 5030 shows some contrast corresponding to edges inthe topography image. This is consistent with the interaction being moreattractive at these regions, again to be expected from surface energyconsiderations (larger areas in proximity will have larger long-rangeattractive forces). Since the fundamental eigenmode amplitude is beingheld relatively constant and there is a relationship between theamplitude and phase, the phase will be constrained, subject to energybalance and the feedback loop that is operating to keep the amplitudeconstant. The second eigenmode amplitude image 5040 shows contrast thatis similar to the fundamental eigenmode phase image 5030. However, thereare some differences, especially over regions thought to be contaminants5041 and 5042. Finally, the second eigenmode phase image 5050 shows themost surprisingly large amount of contrast. The background substrate5053 shows a bright, positive phase contrast. The putative contaminantpatches, 5041, 5042 and 5051 show strikingly dark, negative phase shiftcontrast. Finally, regions where the collagen fibers are suspended 5052show dark, negative phase contrast. In these regions, the suspendedcollagen fibers are presumably absorbing some of the vibrational energyof the second eigenmode amplitude and thus, changing the response.

When an AFM is operated in conventional AC mode with phase detection,the cantilever amplitude is maintained constant and used as a feedbacksignal., Accordingly, the values of the signal used in the loop areconstrained not only by energy balance but also by the feedback loop.Furthermore, if the amplitude of the cantilever is constrained, so willthe phase be constrained. In conventional AC mode it is not unusual forthe amplitude to vary by a very small amount, depending on the gains ofthe loop. This means that, even if there are mechanical properties ofthe sample that might lead to increased dissipation or a frequency shiftof the cantilever, the Z-feedback loop in part corrects for thesechanges in contrast and thus in this sense, avoids presenting thecontrast to the user.

If the technique for using the present invention involves a mode that isexcited but not used in the feedback loop, there will be no explicitconstraints on the behavior of this mode. Instead it will range freelyover many values of the amplitude and phase, constrained only by energybalance. That is to say, the energy that is used to excite thecantilever motion must be balanced by the energy lost to the tip-sampleinteractions and the intrinsic dissipation of the cantilever. This mayexplain the enhanced contrast we observe in images generated with thetechniques of the present invention.

FIG. 6 demonstrates this idea more explicitly. The first image 6010 isan image of the number of pixels at different amplitudes (horizontalaxis) and phases (vertical axis) in the fundamental eigenmode data forthe collagen sample of FIG. 5. As expected, the amplitude values areconstrained to narrow range of ˜0.6Amax by the Z-feedback loop.Constraining the amplitude values in turn, limits the values that thephase can take on to the narrow range around 25°. Thus, when counts atare plotted, there is a bright spot 6020 with only small variations.Small variations in turn imply limited contrast. The second image 6030plots the number of pixels at different amplitudes and phases of thesecond eigenmode for the collagen sample. Here the eigenmode was notconstrained by a feedback loop and it varies from ˜Amax to close tozero. Similarly, the phase ranges over many values. This freedom allowsgreatly increased contrast in the second eigenmode images.

The present invention may also be used in apparatus that induce motionin the cantilever other than through a piezoelectric actuator. Thesecould include direct electric driving of the cantilever (“activecantilevers”), magnetic actuation schemes, ultrasonic excitations,scanning Kelvin probe and electrostatic actuation schemes.

Direct electric driving of the cantilever (“active cantilevers”) usingthe present invention has several advantages over conventional piezoforce microscopy where the cantilever is generally scanned over thesample in contact mode and the cantilever voltage is modulated in amanner to excite motion in the sample which in turn causes thecantilever to oscillate.

FIG. 2 is a block diagram of a preferred embodiment of an apparatus forusing the present invention with an active cantilever. This apparatushas similarities to that shown in FIG. 1, as well as differences. In theFIG. 2 apparatus, like the FIG. 1 apparatus, one frequency source 1080is used to excite motion of the cantilever probe 1020 through amechanical actuator 1040, preferably a piezoelectric actuator, but othermethods to induce cantilever motion known to those versed in the artcould also be used, which drives the chip 1030 of the cantilever probe1020, However, in the FIG. 2 apparatus, the frequency source 1080communicates directly 2010 with the actuator 1040 instead of beingsummed together with the second frequency source 1090, as in the FIG. 1apparatus. The second frequency source 1090 in the FIG. 2 apparatus isused to vary the potential of the cantilever probe 1020 which in turncauses the sample 1010 to excite motion in the cantilever probe 1020 ata different eigenmode than that being excited by the first oscillator1080. The resulting motion of the cantilever probe 1020 interacting withthe sample 1010 will contain information on the sample topography andother properties at the eigenmode excited by the first frequency source1080 and information regarding the voltage dependent properties of thesample at the eigenmode excited by the second frequency 1090. The sampleholder 2030 can optionally be held at a potential, or at ground toenhance the effect.

In one method of using the FIG. 2 apparatus, the amplitude of thecantilever at the frequency of the first source 1080 used as the errorsignal. The amplitude and phase (or in-phase and quadrature components)at the frequency of the second source 1090 or a harmonic thereof willcontain information about the motion of the sample and therefore thevoltage dependent properties of the sample. One example of theseproperties is the piezo-response of the sample.

FIG. 3 is a block diagram of a preferred embodiment of an apparatus forusing the present invention with the second frequency source modulatinga magnetic field that changes a property of the surface. In the FIG. 3apparatus, the situation with the first frequency source 1080 isidentical to the situation in the FIG. 2 apparatus. Instead of thesecond frequency source 1090 being used to vary the potential of thecantilever probe 1020 as with the FIG. 2 apparatus, in the FIG. 3apparatus the second frequency source 1090 modulates the current throughan excitation coil 3010 which in turn modulates the magnetic state of amagnetic circuit element 3020. This element could be used to modulatethe field near an active sample 3030 (not shown) or the excitation coil3010 and magnetic circuit element 3020 could comprise the sample, as inthe case of a magnetic recording head.

The FIG. 3 apparatus can be used with any other sort of ‘active’ samplewhere the interaction between the cantilever and the sample can bemodulated at or near one or more of the cantilever flexural resonancesby one of the frequency sources 1080 or 1090. This could also beextended to high frequency measurements such as described in Proksch etal., Appl. Phys. Lett., vol. (1999). Instead of the modulation describedin that paper, the envelope of the high frequency carrier could bedriven with a harmonic of one or more flexural resonances. This methodof measuring signals other than topographic has the advantage ofrequiring only one pass to complete as opposed to “LiftMode” or Nap modethat require spatially separated measurements of the topographic andother signals.

Another example of a preferred embodiment of an apparatus and method forusing the present invention is from the field of ultrasonic forcemicroscopy. In this embodiment, a high frequency carrier is amplitudemodulated and used to either directly drive the sample or to drive itusing the cantilever as a waveguide. The cantilever deflection providesa rectified measure of the sample response at the carrier frequency.

This embodiment is similar to the conventional force modulationtechnique where the cantilever is typically operated in contact mode. Aswith other contact mode techniques, however, the force modulationtechnique has the disadvantage that the forces acting between the tipand the sample can be quite significant, often resulting in damage tothe tip or sample and reduced spatial resolution.

However, because the ultrasonic force embodiment described here is an ACimaging method, the damage to the tip and/or sample is significantlyreduced as compared to contact mode techniques. Thus, one or moreeigenmodes are used for the Z-feedback loop, taking the place of thecontact mode feedback loop, and one or more additional eigenmodes can beused to measure the high frequency properties of the sample.

The described embodiments of the invention are only considered to bepreferred and illustrative of the inventive concept. The scope of theinvention is not to be restricted to such embodiments. Various andnumerous other arrangements may be devised by one skilled in the artwithout departing from the spirit and scope of the invention.

The invention claimed is:
 1. An atomic force microscope operating todetermine voltage dependent properties of a sample, comprising: acantilever having a probe tip; an actuator for the cantilever, that isdriven to move said cantilever; a first frequency source driving saidactuator for the cantilever at a first frequency; a second frequencysource varying an electrical potential of the cantilever relative to thesample at a second frequency, different than the first frequency; and adetector detecting cantilever response information to the sample at bothvalues related to said first frequency and said second frequency,wherein said detector measures an amplitude and phase of first andsecond eigenmodes of the cantilever as a measured characteristics of thesample.
 2. The microscope as in claim 1, further comprising a connectionfor grounding said sample.
 3. The microscope as in claim 1, wherein saidactuator drives said cantilever to avoid touching the sample.
 4. Themicroscope as in claim 1, wherein said cantilever response informationincludes values at said first and/or second frequencies or harmonicsthereof.
 5. The microscope as in claim 1, wherein said actuator drivesthe cantilever at or near a flexural resonance thereof.
 6. Themicroscope as in claim 1, wherein said detector measures an amplitude ofthe cantilever at the first frequency as an error signal, and alsomeasures information at said second frequency or a harmonic thereof torepresent voltage dependent properties of the sample.
 7. A method ofdetermining both topographic and material dependent properties of asample, comprising: exciting a cantilever probe at a first frequencyusing a first frequency source driving a first actuator to drive thecantilever at said first frequency; using a second frequency source at asecond frequency different than said first frequency, to vary anelectrical potential of said cantilever probe and thereby cause saidsample to excite motion in said cantilever probe; detecting aninteraction of said cantilever probe with said sample at values relatedto said first frequency and said second frequency; and using interactioninformation indicative of said interaction, determining topographic andother information about said sample and simultaneously determiningvoltage dependent and other material properties of the sample, whereinsaid detecting comprises measuring an amplitude and phase of first andsecond eigenmodes of the cantilever to provide information about aresponse of said sample interacting with a tip of the cantilever probe.8. A method as in claim 7, wherein said second frequency varies avoltage on the cantilever probe relative to the sample.
 9. A method asin claim 8, further comprising grounding said sample.
 10. A method as inclaim 7, wherein said second frequency varies a magnetic field on thesample.
 11. A method as in claim 7, wherein said cantilever is driven toavoid touching the sample.
 12. A method as in claim 7, wherein saidinteraction response information includes values at said first and/orsecond frequencies or harmonics thereof.
 13. A method as in claim 7,wherein said second frequency varies an ultrasonic field on the sample.14. A method as in claim 13, further comprising using said cantilever asa waveguide for applying an ultrasonic wave to the sample an ultrasonicfield.
 15. An atomic force microscope, comprising: a sample holder, witha surface that holds a sample; a cantilever probe, having a tip that maybe located near said surface; a first actuator, which drives thecantilever probe at a first frequency; a first frequency sourcecontrolling said first actuator; a second frequency source at a secondfrequency different than the first frequency, varying an electricalpotential of the cantilever probe and thereby causing said sample toexcite motion in said cantilever probe; and a detector, detecting aresponse of said cantilever probe interacting with said sample at valuesrelated to said first frequency and said second frequency, said detectorproducing topographic and other information about said sample, and alsovoltage dependent and other material properties of said-sample, whereinsaid detecting comprises measuring an amplitude and phase of first andsecond eigenmodes of the cantilever to provide information about theresponse, where the response is of said sample interacting with a tip ofthe cantilever probe.
 16. A microscope as in claim 15, furthercomprising a connection grounding said sample holder.
 17. A microscopeas in claim 15, wherein said second frequency varies a voltage on thecantilever probe relative to the sample.
 18. A microscope as in claim15, wherein interaction information includes values at said first and/orsecond frequencies or harmonics thereof.
 19. A microscope as in claim15, wherein said detecting comprises measuring an amplitude of thecantilever at said first frequency as an error signal, and measuringinformation at said second frequency or a harmonic thereof to representvoltage dependent and other material properties of the sample.